Sharif Digital Repository

Here, we first ivestigate some available nonsmooth algorithms indentilying their drawbacks, and then provide some guidelines to avert these drawbacks. We divide the algorithms to two main classes, first order and second order. The main drawback of the second order class of algorithm is that there does not exist any suitable method to approximate the generalized second order derivative. To solve this problem, we construct a uniform approximation for the generalized Hessian matrix of an SC1 function. Using the discrete gradient and the extended second order derivative, we define the discrete Hessian matrix. We construct a sequence of sets, where each set is composed of discrete Hessian... 

The heavy ion collision experiments are in progress in order to investigate how the Universe has evolved after the Big Bang. The recent observations show that a nearly perfect fluid is produced after heavy ion collisions. An appropriate incorporation of the relativistic hydrodynamics and the field theory would help us to describe the dynamics of QCD (Quantum Chromodynamics) matter under extreme conditions, and to survey the expected phase transitions. The majority of efforts to investigate the characteristics of the QCD plasma are devoted to an ideal, non-dissipative one. To get the results which are highly in accordance with the experiment, it is necessary to bring also in mind the role of... 

Design, analysis and practical implementation of the filter trust-region algorithms are investigated. First, we introduce two filter trust-region algorithms for solving the unconstrained optimization problem. These algorithms belong to two different class of optimization algorithms: (1) The monotone class, and (2) The non-monotone class. We prove the global convergence of the sequence of the iterates generated by the new algorithms to the first and second order critical points. Then, we propose a filter trust-region algorithm for solving bound constrained optimization problems and show that the algorithm converges to a first order critical point. Moreover, we address some well known... 

These days steel frames are among the most widespread structural systems, and apart from this, tendency for using slender members in these frames, shows the need for study of effects of axial force and in other words stability of the structure and its members. When secondary effects due to axial gravity forces which results in lateral displacement of the structure come in action, they will reduce strength significantly; as a consequent ductility demand with raise. If this decreased strength exceeds the existing redundant strength, displacements will increase significantly and cause instability of the structure and its collapse. AISC 360-10 has introduced 3 methods for analyzing stability of... 

The recent researches show that Value at Risk estimations are biased and is calculated conservatively. Bao and Olah (2004) proved that the bias of an ARCH(1) model for VaR can be formulated in to two parts: bias due to return Misspecification ( ) and bias due to estimation error ( ). Using a GARCH(1,1) and quasi maximum likelihood estimation method, this research intends to find an analytical framework for the two source of biases. We generate returns from Normal and t-student distributions, then estimate the GARCH(1,1) under Normal and t-student assumptions. Our findings reveal that equals to zero for the Normal likelihood function, but . Also, and are not zero for the t-student... 

In this thesis, we study monadic second order logic and the languages of graphs. We introduce the notion of ∆- regular graph automaton. Then we designed this finite automaton for processing on labeled graphs. Definability of graph languages which are recognizable by this automaton is shown. To do this, we first briefly introduced monadic second order logic, and then we studied definability of regular string and tree languages in monadic second order logic. In the last section of thesis, ∆- regular graph automaton is introduced  

The use of steel as one of the most widely used materials in the construction of structures is accompanied by problems and among them the problem of establishing stability in structure is important. To provide stability in the structure as a whole and for each of its elements, the new edition of the American Specification for Structural Steel Buildings, has introduced three general methods based on the elastic analysis. It includes, direct analysis method, effective length method and first-order analysis method. Each method has advantages and disadvantages. The present study is divided into two parts. The first part gives an overview of the behavior of structures and methods of determining... 

Proper operation of a spark ignition engine is required by comfort demands of a vehicle driver and governmental legislations. Therefore it is essential to monitor, within an online technique, the engine and detect any fault which disrupts its operation. The gas exchange path (including the intake and exhaust subsystems) is an important part of turbocharged engines responsible for accurate control of both engine power and emissions. Monitoring the path for fault detection and isolation (FDI) has been always demanded due to many failures it may face since the turbocharger exasperates the harsh working conditions for components involved in the path. This paper presents a novel model-based... 

Factor analysis based methods are one of the applied methods in the Chemometrics. In this regard, some modifications on one of the factor analysis based method named fixed size moving window evolving factor analysis were done and two new methods named variable size moving window evolving factor analysis and preselected variable size moving window evolving factor analysis were introduced. The performance of the new introduced methods were examined and compared by the fixed size moving window evolving factor analysis.
Pure variable selection methods are useful for curve resolution methods which need to define an initial estimate from chromatographic profile or spectra. In this aspect the... 

There are considerable investigations on wettability alteration in carbonate reservoirs in recent years. The presence of ions including Ca, Si, Al etc in natural carbonate rocks and also the presence of various fatty acids, resins, asphaltenes etc in crude oil makes it difficult to understand the complex mechanism of wettability alteration by using surfactants. Furthermore there is still a conspicuous lack of dynamic wettability alteration model to demonstrate the dynamic behavior of cationic surfactants during wettability alteration. It is also widely accepted that cationic surfactants have substantial impact on changing the wettability of strongly oil-wet matrixes to a more water-wet... 

In this thesis, we study the resilience of complex systems under structural perturbations. After a brief review of the resilience and its importance, we show that how one can map a system of N-coupled dynamical equations onto an effective one-dimensional dynamics. This procedure is based on a nearest neighbor averaging. The obtained map, helps us study the response of the system to the effective one-dimensional control parameter, instead of all parameters that are affecting the structure of the network. Next, we use this procedure and unveil the resilience pattern of second-order Kuramoto oscillators on complex networks. Moreover, we propose a control strategy for complex systems which is... 

Guilt aversion, the process of avoiding guilt, when guilt indicates the human sense which is present when they let down other's expectations. As the definition suggests, guilt is related to what one thinks of the others’ thoughts; i.e. the second-order beliefs. Incomplete information models of guilt aversion are the most reliable ones in the literature due to economic experiments. Based on these models, the dictator game and the trust game are applied to measure the degree of guilt aversion. In both the above psychological games, there are two players where Player A has the power to decide about the split of the money. We use the amount of transferred money to Player B is as a sign of guilt... 

Control of complex networks is the main topic in this study. In this thesis, we consider the methods to steer the dynamics of a network from an initial state to the desired final state. To achieve this goal, one needs to inject appropriate control signals from some of the network nodes, known as driver nodes. We consider the quadratic sum of control signals as a cost function, to control the dynamics of the network. By minimising the cost function, we obtain the control signals as well as driver nodes for a linear time-invariant system. As an example, we provide the results of an energy minimization strategy to control the second order Kuramoto and Rössler dynamics in Erdos-Renyi and... 

Stabilized sequential quadratic programming (sSQP) methods for nonlinear optimization generate a sequence of iterates with fast local convergence regardless of whether or not the activeconstraint gradients are linearly dependent. Here, we are concerned with the local convergence analysis of an sSQP method, recently introduced in the literature, that uses a line search with a primal-dual augmented Lagrangian merit function to enforce global convergence. The method is provably well-defined and is based on solving a strictly convex quadratic programming subproblem at each iteration. It is shown that the method has superlinear local convergence under assumptions that are not stronger than those... 

The main goal of controlling overhead crane systems is to safely transfer the load to its desired position with maximum speed and accuracy, as well as to minimize or eliminate load oscillations. The overhead crane system is considered as an underactuated mechanical system in which the number of control inputs (actuators) is less than the number of degrees of freedom. In addition, overhead crane systems are generally associated with parametric or unmodeled uncertainties. Also, in these systems, external disturbances such as wind have a destructive effect on the system's performance. In addition, if the overhead crane has the hoisting mechanism and the length of the rope changes as the trolley...